The computational efficiency of flow simulations with Multi-resolution analysis (MRA) was enhanced via the boundary treatment of the computational domain. In MRA, an adaptive dataset to a solution is constructed through data decomposition with interpolating polynomial and thresholding. During the decomposition process, the basis points of interpolation should exceed the boundary of the computational domain. In order to resolve this problem, the weight coefficients of interpolating polynomial were adjusted near the boundaries. By this boundary treatment, the computational efficiency of MRA was enhanced while the numerical accuracy of a solution was unchanged. This modified MRA was applied to two-dimensional steady Euler equations and the enhancement of computational efficiency and the maintenance of numerical accuracy were assessed.